QN: A person with IQ score greater than 145 is considered to be genius. Does the empirical rule support this statement? Explain. [Given is: the IQ score has bell shaped distribution with a mean of 100 and standard deviation 15]
Ø  Here,
Given that,
Mean= 100
Standard deviation= 15
Since the IQ score has bell shaped curve/ normal distribution,
The z value will be,
Z=(x- µ)/σ
  = (145-100)/15
  = 3


Since,
P(X>145)
=P (0<Z<ꚙ)-P (0<Z<3)
=0.5-0.4987
=0.0013
Yes, the empirical rule supports the statement and follows normal distribution. According to the given data only 0.13 % people are genius.







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